Has OpenAI used the work of mathematicians to solve the Millennium Prize problem?

OpenAI claims to solve the Navier-Stokes existence and smoothness problem, but faces a crisis of public trust

OpenAI claims to have solved the Navier-Stokes existence and smoothness problem. This is one of seven "Millennium Award puzzles" proposed by the Scientific Advisory Board of the Clay Mathematical Institute (CMI) in Cambridge, Massachusetts. However, a more difficult task than solving mathematical problems may be proving its innocence to a public that is increasingly skeptical of the giant artificial intelligence laboratory's methodology.

Just as OpenAI has just solved one of the most difficult unsolved mathematical problems of our time, it has to face the question of two mathematicians: whether their unpublished research has somehow helped the laboratory come up with the answer. As this dramatic event unfolded in the public eye, as expected, when a trillion-dollar AI laboratory that was mired in controversy over reckless proxy security breaches and internal "security reflections" on risk handling faced two more affinity scholars, OpenAI was clearly a few steps behind in terms of public opinion perception.

Which mathematical problem has OpenAI solved?

The AI laboratory, led by Ultraman, said it has written a proof process and provided a version that can be machine checked in the Lean proof language. The proof shows that under the action of smoothing forces, a smooth fluid that is initially calm can accelerate infinitely in a limited time and eventually collapse.

OpenAI claims that the work was done by its internal model, which has computing power that exceeds the recently released GPT-6 Astra model. This result solved one of the seven million dollar problems listed by the Clay Mathematical Institute in 2000. According to Research Director Mark Chen, OpenAI's computing fees exceeded the $1 million bonus provided by CMI. Laboratory researcher Sebastien Bubeck said that at one point, about 10,000 agents were working together to deal with the problem.

Currently, the Clay Institute has not recognized OpenAI's proof. The institute stipulates that solutions must be published on qualified publishing channels, open to the public for two years, and be widely recognized by the mathematician community to be eligible for prize review. It is worth noting that OpenAI has made it clear that it will not seek the bonus.

Does OpenAI use mathematicians 'research results in chat logs?

The main controversy surrounding OpenAI's work is not even the mathematics itself. The real dramatic conflict is whether the information input into AI models, including OpenAI Codex, by Tristan Buckmaster at New York University and Lvent Alpöge, a mathematician hired by Anthropic, has been stolen or misappropriated.

When Tristan first learned that the AI laboratory was using a large amount of computing resources to solve the Navier-Stokes problem, he directly asked laboratory researchers whether the records of their Codex conversations with Lvent were used. Like a typical mathematician, Tristan avoided making any accusations without evidence, writing in a public statement: "I don't know if our data was used."

However, the same document accuses OpenAI of making "proposals" that included removing Lvent's name from solution announcements related to OpenAI's internal model. Bubeck later refuted this, writing on Platform X (formerly Twitter):"I have never and will never ask to remove Lvent from the list of authors of his own work." He clarified that the screenshot showed him coordinating the release with Lvent and said they were acting with the best intentions.

Sam Ultraman also stepped forward to support his team. But to skeptics, denials such as "unlikely but not impossible" seem weak.

OpenAI's core defense is very clear: neither human employees nor its agents saw their prompts, drafts or user data, and they were not exposed to relevant content until after the work was made public. However, in its official blog post, the company added a line that caught Lvent's own attention: "Although unlikely, we cannot rule out that de-identified data derived from user use of our products can help improve our model." "Anyway, thank you for their candor," Lvent commented.

Tristan's narrative also complicates OpenAI's narrative. He said he was initially told that there was "very little human participation" in the result, but during the phone call he revealed that a full team was involved and started with simpler questions. He even pointed out that the prompt words shown to him were themselves generated through the prompt Codex. He attributed credit for the underlying program to the mathematicians Diego Córdoba and Luis Martínez-Zoroa, calling this moment a "deep blue-Kasparov" turning point in the field.

As of now, Tristan has not filed a lawsuit. OpenAI maintains that its proof is significantly different from the two men's work and that no user data was accessed during the generation process.

As more and more research is conducted through AI systems owned by rival companies building tools, the more difficult question is no longer who has the final idea, but what the platform can do with what is entered into it and how to prove the existence of this effect afterwards.